With one game left AEK are second behind Olympiakos Piraeus, who have already secured the title, with 66 points, two more than third-placed Panathinaikos who won 4-0 at home to Egaleo.
Panathinaikos coach Alberto Malesani has already paid the price for the club's relatively mediocre season and the man who is set to take over from him, Swedish coach Hans Backe, was at the game to run his eye over his new team.
Sources at the club say Backe has already signed a one-year contract, with the option of a second year, but Panathinaikos will not make an official statement until the end of the season.
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An early strike from Fanis Gekas sent them on their way before an own goal after 25 minutes and two second-half strikes by Dimitris Papadopoulos eased them to a comfortable win.
The battle to avoid the final relegation spot will go to the last day of the championship after the three contenders, Levadiakos, Panionios and OFI Crete, all won on Sunday.
Akratitos and Kallithea are already down and OFI, third from bottom with 28 points, remain the favourites to join them. Their final game is at home to Levadiakos who have 31 points.
Between them on 29 points are Panionios, who have a final trip across Athens to play Egaleo.
Levadiakos produced the most surprising result by stunning the champions Olympiakos 3-2 with goals in the first 17 minutes from Nikos Dimitropoulos, Alban Bushi and Ivan Rusev.
Olympiakos came back strongly in the second half with Milos Maric pulling one back in the 48th and Michalis Konstantiadding a second goal on the hour.
But Levadiakos held on and need only draw their final game against OFI to be absolutely certain of staying up.
Goals from Joseph Nwafor and Metodi Dejanov either side of halftime gave OFI a 2-0 lead over PAOK and they held on to win despite Yiasoumis Yiasoumi's 75th minute goal for the visitors.
Panionios made a mockery of their league position with a convincing 3-0 win over fourth-place visitors Iraklis.
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